An argument is a set of claims (called “premises”) offered in support of a conclusion. I said you should go to bed. Premises I’m your mother. Types of ---------------------------------- Arguments So, you should go to bed. Conclusion An argument’s conclusion is often the most controversial claim in the argument. The job of the Justin C. Fisher premises is to ease people into accepting the conclusion. Conclusions are often indicated by words like “therefore”, “thus”, “hence” or “so.” What makes an argument good? Three types of arguments/support Obama has X-ray vision Deduction – provides a guarantee that Obama is a martian. IF the premises are true, then the conclusion must also be true. ----------------------------------------------------- So at least one martian has X-ray vision. The premises must be true. Induction – generalize from a sample of things, to conclude that some other thing(s) will be like the sample. Roses are red. -------------------------- Abduction (Inference to best explanation) So violets are blue. – conclude that the best explanation for some observation(s) is probably true The premises must support the conclusion. 1
Deductively valid arguments come with a guarantee: “if all the premises are true, then the conclusion must be true.” Deduction, C All A’s are B’s. B Validity, and Soundness All B’s are C’s A ------------------------------ So all A’s are C’s. Note: you can determine whether an Justin C. Fisher argument is valid without knowing whether its premises actually are true. Obama is a democrat. Many democrats are black. Obama is a martian. ------------------------------------ Obama has X-ray vision. Obama is black. ------------------------------------------- So at least one martian has X-ray vision. The premises in this argument are true, and the conclusion is true. The premises in this argument aren’t true. But, the premises, by themselves, But, if they were true, then the conclusion do not guarantee that the would be too. So this argument is valid . conclusion would have to be true. To be SOUND an argument needs to both So this argument is Invalid. (1) be valid and (2) have only true premises. This argument is UNSOUNd. 2
An argument can still be Obama is a martian. George flurbs. valid even if a premise is F R Obama has X-ray vision. George is a rogon. false! But it can’t be sound. ------------------------------------------- ------------------------------------- (Every semester students G eorge So at least one martian So at least one rogon flurbs. mess this up!) has X-ray vision. Even though we don’t know who George is, The premises in this argument aren’t true. what a rogon is, or what it is to flurb, we can still tell that, if the premises are true , then But, if they were true, then the conclusion the conclusion must be true. So this would be too. So this argument is valid . argument is valid. To be SOUND an argument needs to both But we can’t tell whether or not it is SOUND. (1) be valid and (2) have only true premises. This argument is UNSOUNd. Test #1 for invalidity: Try to imagine a Test #2 for invalidity: Pick a noun/adjective possible way that the premises could be true in the argument and substitute in some new while the conclusion is false. noun/adjective everywhere it appeared. female strippers 1. All great singers look great. 1. All great singers look great. 2. Robin looks great. -------------------------------- 2. Robin looks great. C. So Robin is a great singer. -------------------------------- female stripper Make 1 true: Kill off any ugly singers. C. So Robin is a great singer. Make 2 true: (Not too hard.) Substitute “great singer” � “female stripper” Make C false: remove Robin’s vocal cords. The resulting argument obviously isn’t valid. Since the premises could be true while the So the original argument wasn’t valid either. conclusion is false, this argument is Invalid . 3
Test #3 for invalidity: Draw the argument as Some common argument forms: a Venn diagram in such a way that you keep the premises true, but make the C false. Q Q All P’s are Q’s. All P’s are Q’s. Great x is a Q. . lookers. P x is a P. . 1. All great singers look great. P x x is a P. x is a Q. Great 2. Robin looks great. singers. ---------------------------------------- C. So Robin is a great singer. Q x Q All P’s are Q’s. All P’s are Q’s. x Premise 1 tells us the great singers are contained x is not a P. . x is not a Q. . P P within the great lookers. x is not a Q. x is not a P. Premise 2 tells us Robin is inside the larger circle. But it doesn’t guarantee that he is also in the smaller circle � Invalid . Q Q The arguments Q If P then Q All P’s are Q’s. If P then Q x below are equivalent P Q . x is a P. . P . P P in logical form to this x one, and are valid for P x is a Q. Q x the same reason. All scenarios where P is true are ones where Q is true. Our scenario is one where P is true . . x Q If P then Q If P then Q Q x Our scenario is one where Q is true . not P . not Q . P P If P then Q not Q not P. P . Q 4
Deductive Arguments Can Be Useful A big limitation on valid arguments P1. Every natural event has a preceding cause. A valid argument typically can’t include any concepts P2. There can’t be an infinite chain of causes. in the conclusion that aren’t in the premises. ------------------------------------------------------------ – Premises about how the drug performs in some C. So there must have been some event whose cause people can’t guarantee how it will perform in was super-natural. other people . ( � induction is more useful) Once somebody puts forward an argument like – Premises about observable things, like how the this, we have just three choices: bulb glows when you connect the wires, can’t (1) Say the argument isn’t valid. guarantee conclusions about the existence of (2) Reject one (or more) of the premises, or invisible electrons. ( � abduction is more useful) (3) Accept the conclusion. It may sometimes help to consider valid arguments, but these arguments won’t be very useful for (If we accept that it is valid and has true premises, reaching many positive scientific conclusions. that would guarantee its conclusion is true.) Inductive Arguments A sample of A’s have been B’s. ------------------------------------------------------------ Induction: So (probably) all A’s are B’s. Expecting things you haven’t - generalize from a sample to other things. - the conclusion re-uses words/concepts seen to be like things you have that were observed to be true of the sample. - provide only a weak guarantee: “If the premises are true, then the conclusion is Justin C. Fisher probably true.” 5
How to make an inductive argument Step 1. Find a sample that would be representative of what you want to draw a conclusion about. P1. We randomly selected 500 voters from Florida. P2. A strong majority of our Step 2. Observe what traits things in your sample prefer Donald. sample have. --------------------------- Step 3. Conclude that C. So, a strong majority of all one or more other things voters in Florida probably will have those traits too. prefer Donald too. Induction in Science Assessing Inductive Arguments – Scientists often presume laws of nature work How large is the sample? the same way in all places and times, so Would you trust a poll of 10 voters? 10,000? experiments at one place and time will How representative is the sample? (i.e., generalize to others. how likely is it that the things in the sample – Drug trials can’t guarantee that a drug will work would be like the things in the conclusion?) similarly in other people, but they can provide Poll Kansans to predict how Oklahomans will vote? strong reason to think it probably will. How about polling New Yorkers? However, induction just gives us “more of the same,” just generalized to other places or times. Was the choice of sample-members biased? – We still haven’t seen any way for scientists to Many polls involve telephone calls to land-lines. get from premises about experimental This under-represents cell-phone users, people observations to conclusions about something who aren’t home much, people who lack phones. entirely different, like invisible electrons. 6
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